1. Preheat the grill or broiler to high. Wash and dry the chicken breasts and trim off any fat and sinews. Brush the chicken breasts with olive oil and thickly sprinkle with cracked peppercorns and salt. Grill the breasts until cooked, 2 to 3 minutes per side. Transfer the chicken breasts to a cutting board and thinly slice widthwise across the grain. If using cooked chicken, thinly slice or dice it.
2. Place the potatoes in a pot with cold water to cover and salt. Bring the potatoes to a boil, reduce the heat, and simmer until tender, 8 to 10 minutes. Refresh the potatoes under cold water and drain. Cut any large potatoes in quarters or halves to have bite-size pieces. Snap the stems off the beans and cook them in rapidly boiling salted water until crispy-tender, about 2 minutes. Refresh under cold water and drain.
3. Fan the tomato slices out to cover the bottom edges of 4 large plates or a platter. Mound the mesclun at the top of the plate. Arrange bundles of haricots verts, clusters of potatoes, and piles of olives between the tomatoes and mesclun. Sprinkle the hard-cooked egg whites and sliced onion on top. Or use a different arrangement: The idea is to create a pretty, colorful salad.
4. Prepare the vinaigrette. Place the stock, vinegar, olive oil, garlic, scallion, anchovy fillets (if using), capers, and basil leaves in a blender and puree until smooth. Correct the seasoning, adding black pepper and salt to taste. (You probably won’t need salt if you use the anchovy.) Transfer the dressing to a bowl and serve on the side.